Skip to main content
Log in

Non-Archimedean Quasitriangular Operators and the Invariant Subspace Problem

  • Research Articles
  • Published:
p-Adic Numbers, Ultrametric Analysis and Applications Aims and scope Submit manuscript

Abstract

In this paper, we are interested in the study of non-Archimedean quasitriangular operators and their relation to the invariant subspace problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Aguayo and M. Nova, “Non-archimedean Hilbert like spaces,” Bull. Belg. Math. Soc. Simon Stevin 14, 787–797 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  2. Y. Amice, “Interpolation \(p\)-adique,” Bull. Soc. Math. France 92, 117–180 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Apostol, “Quasitriangularity in Hilbert space,” Indiana U. Math. J. 22, 817–825 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Apostol, C. Foia and D. Voiculescu, “Some results on nonquasitriangular operators,” Rev. Roum. Math. Pures Appl. IV, 285–312 (1973).

    Google Scholar 

  5. W. B. Arveson and J. Feldman, “A note on invariant subspace,” Michigan Math. J. 15, 61–64 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Babahmed and A. El Asri, “Invariant subspace problem and compact operators on non-Archimedean Banach spaces,” Extr. Math. 35, 205–219 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Diagana and F. Ramaroson, Non-Archimedean Operator Theory, Springer Briefs Math. (Springer, Cham, New York, 2016).

    Book  MATH  Google Scholar 

  8. R. G. Douglas and C. Pearcy, “A note on quasitriangular operators,” Duke Math. J. 37, 177–188 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  9. P. R. Halmos, “Invariant subspaces of polynomially compact operators,” Pacif. J. Math. 16, 433–437 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  10. P. R. Halmos, “Quasitriangular operators,” Acta Sci. Math. 29, 283–293 (1968).

    MathSciNet  MATH  Google Scholar 

  11. G. R. Luecke, “A new proof of a theorem on quasitriangularoperators,” Amer. Math. Soc. Proc. 36, 535–536 (1972).

    Article  MathSciNet  Google Scholar 

  12. P. Meyer-Nieberg, “Quasitriangulierbare operatoren und invariante untervektorraume stetiger linearer operatoren,” Arch. Math. (Basel) 22, 186–199 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  13. L. R. Narici and E. Beckenstein, “A non-Archimedean inner product,” Contemp. Math. 384, 187–202 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  14. C. Pearcy and N. Salinas, “An invariant-subspace theorem,” Michigan Math. J. 20, 21–31 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  15. C. Perez-Garcia and W. H. Schikhof, Locally Convex Spaces over Non-Archimedean Valued Fields, Cambridge Stud. Adv. Math. 119 (Cambridge University Press, Cambridge, 2010).

    Book  MATH  Google Scholar 

  16. W. Sliwa, “The invariant subspace problem for non-Archimedean Banach spaces,” Canad. Math. Bull. 51, 604–617 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  17. A. C. M. Van Rooij, Non-Archimedean Functional Analysis, Monograph Textbooks Pure Appl. Math. 51 (Marcel Dekker, Inc., New York, 1978).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Azzedine El Asri or Mohammed Babahmed.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

El Asri, A., Babahmed, M. Non-Archimedean Quasitriangular Operators and the Invariant Subspace Problem. P-Adic Num Ultrametr Anal Appl 14, 325–334 (2022). https://doi.org/10.1134/S2070046622040069

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070046622040069

Keywords

Navigation